Finite Element Analysis
ENG ME 707
An introduction to the finite element method with emphasis on fundamental concepts. Variational equations, Galerkin's method. Finite element applications to linear elliptic boundary value problems in structures, solid and fluid mechanics, and heat transfer. Optimality, convergence, function spaces and energy norms. Isoparametric elements. Mixed methods, penalty methods, selective reduced integration; applications may include Kirchoff plate theory, incompressible elasticity, Stokes flow. Thick and thin beams, plates, and shells. Implementation: element data structures, numerical integration, assembly of equations, element routines, solvers. Advanced topics may include dynamic analysis, stabilized methods, eigenvalue problems, and hybrid analytical methods.